Archiv der Mathematik

, Volume 73, Issue 6, pp 465–473

Random projections of regular polytopes

  • K. Böröczky, Jr.
  • M. Henk

DOI: 10.1007/s000130050424

Cite this article as:
Böröczky, Jr., K. & Henk, M. Arch. Math. (1999) 73: 465. doi:10.1007/s000130050424


Based on an approach of Affentranger & Schneider we give an asymptotic formula for the expected number of k-faces of the orthogonal projection of a regular n-crosspolytope onto a randomly chosen isotropic subspace of fixed dimension, as n tends to infinity. In particular, we present a precise asymptotic formula for the (spherical) volume of spherical regular simplices, which generalizes Daniel's formula.

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • K. Böröczky, Jr.
    • 1
  • M. Henk
    • 2
  1. 1.Mathematical Institute of the, Hungarian Academy of Sciences, H-1364 Budapest, P.O.B. 127, HungaryHU
  2. 2.University of Magdeburg, Department of Mathematics/IMO, Universitätsplatz 2, D-39106 Magdeburg, GermanyDE